Re: Thyseneal: V 3.6 ::REVAMP::

[ender516]

I got wrapped up with other things this evening and so I have not had time to analyze this in detail. I hope to check it out tomorrow evening.

EDIT:

Well, a day has come and gone and I did get a look at this, and I think I understand the problem now. I had been checking bonus probabilities with a copy of MrBenn's spreadsheet. I had to expand it a bit to handle all the zones on this map, and I guess I broke it, because I ended up with something that didn't calculate the probabilities the same way in different parts of the sheet.

Anyway, I played around a little more, keeping in mind that the starting positions reduce the map effectively to 43 regions to be split among the players. Also, because Dalmus is part of a starting position, the probability of getting the Islands bonus becomes more complex. In a 3 player game, one player definitely has Dalmus, and then must pick up at least two of the remaining four islands, which has a probability of occurring 29.9% of the time. The other two players must get three of the four islands apart from Dalmus, and each of them has a 8.6% chance of doing that. Altogether, this gives about a 47% chance of somebody getting that bonus. There are two 4-region zones and for the player getting Scaralact in a starting position the Skyatica bonus is effectively one as well. In a two or three player game, the probability of dropping a 4-region zone in the 14 regions that one gets out of 43 is 0.81%, but that is multiplied by the number of players that have a shot, so that is 3 times the two regions and the one shot at Skyatica, so we get 7 times 0.81% or 5.67%. All of these probabilities would seem to explain why so many games are starting with bonuses in the drop. I'm not sure what our best solution would be, and I am a little too tired to sort one out just now, but I suspect we might want to bring the islands into the starting positions. We also have the problem that in a two player game, the regions in the unused starting position are returned to the pool, so we have 46 regions divided three ways (the two players, plus a share of neutrals). That means the two players each start with 18 regions, for an initial deployment of six. This is bad for the second player, since the first player could quite easily take a region and drive the second player's deployment down to five.

[mattattam]

You're math is off on the amount of territories that players start with for a 2 player game. They start with 16 each. Same goes for 3 player games (16 each)

This is my proposal as stated earlier:

mattattam wrote:Proposal (discussed above)

Proposal: Make 2-3 player games starting territory positions 14 territories (currently 16 each) and 4 player games starting territories 11 each (currently 12 each)

Reason: To balance first turn advantage more evenly and decrease probability of dropping bonus

The question Bison asked is can we put two different amounts for starting positions? (14 for 2-3 player games and 11 for 4 player games)
At the very least the amount of starting territories can be taken from 16 to 14 in 2-3 player games right? Although I do not know how the technical aspect of creating this works I'm sure there is some way you can change this.

[ender516]

My math is correct. Check a recent game like Game 7871873 and you can see that green, playing first, had 18 regions.
There are 52 regions on the map, with 3 starting positions each containing 3 regions, leaving 43 regions in a pool for random distribution. So with two players, two of the three positions are handed out to the players, and the regions in the remaining position are returned to the pool, leaving 46 regions to be divided by three (one third to each player, and the remainder left neutral).

As far as 3 player games go, look for example at Game 7833975. Each of the three players gets one starting position of three regions, then the pool of 43 is split three ways, for 14 more regions each (17 in total each), with one region left neutral.

Now that danryan's game, Game 7857092, has completed, we can see that Leehar did in fact drop Lyalia and the Islands. With the Islands bonus only requiring 3 out of 5 regions, and one of them, Dalmus, being a part of the starting positions used to prevent the drop of the Chunjaris-Theraland road bonus, we now have a high probability of a player dropping it, as I outlined above.

In order to have 4-player games start with 11 regions each, presuming no changes to the current scheme of 3x3 starting regions, the total number of regions in the pool would have to be between 44 and 47 inclusive. This would require 6 to 9 regions designated to start neutral.

In order to have 2- and 3-player games start with 14 regions, presuming no changes to the current scheme of 3x3 starting regions, the total number of regions in the pool would have to be between 33 and 35 inclusive (yielding 11 regions to add to the 3 regions in a starting position). This would require 8 to 10 regions designated to start neutral.

So, choosing 8 or 9 neutrals would give the starts that mattattam proposes.

An entirely different approach to our problems might be to simply make all the cities start as neutral 2's. No one can drop a road bonus, or any other bonus, apart from the Islands. Divide the non-city islands with a set of starting positions, and the drops should be much more fair.

[The Bison King]

n order to have 2- and 3-player games start with 14 regions, presuming no changes to the current scheme of 3x3 starting regions, the total number of regions in the pool would have to be between 33 and 35 inclusive (yielding 11 regions to add to the 3 regions in a starting position). This would require 8 to 10 regions designated to start neutral.

So, choosing 8 or 9 neutrals would give the starts that mattattam proposes.

An entirely different approach to our problems might be to simply make all the cities start as neutral 2's. No one can drop a road bonus, or any other bonus, apart from the Islands. Divide the non-city islands with a set of starting positions, and the drops should be much more fair.

What I need to know is how would this effect 6-8 player games? Would the amount of territories players receive in those games be reduced do to these changes?

[mattattam]

I see the recent games ender with 2-4 player games. Got it.

I'm on the fence about the idea of making the cities start neutral 2. This would drastically change gameplay where you would have to take a city to get any bonus. This could be good though and make this map very unique. The idea that you wouldn't be able to drop a bonus is very attractive idea since it would drastically cut down first turn advantage.

The only concern would be the Chunjaris to Theraland bonus which is comprised of 3 territories and are all cities.
Also the question of how it affects 5-8 player games is important but not my area.

[ender516]

n order to have 2- and 3-player games start with 14 regions, presuming no changes to the current scheme of 3x3 starting regions, the total number of regions in the pool would have to be between 33 and 35 inclusive (yielding 11 regions to add to the 3 regions in a starting position). This would require 8 to 10 regions designated to start neutral.

So, choosing 8 or 9 neutrals would give the starts that mattattam proposes.

An entirely different approach to our problems might be to simply make all the cities start as neutral 2's. No one can drop a road bonus, or any other bonus, apart from the Islands. Divide the non-city islands with a set of starting positions, and the drops should be much more fair.

What I need to know is how would this effect 6-8 player games? Would the amount of territories players receive in those games be reduced do to these changes?

With 52 regions and 8 or 9 neutrals, you have 43 or 44 regions to divide among the players.

With 44, in 4-player, each gets 11; in 5-, each gets 8, and the extra 4 become neutral as well; in 6-, each gets 7, and the extra 2 become neutral; in 7-, each gets 6, and the extra 2 become neutrals; and in 8-, each gets 5, and the extra 4 become neutrals.

With 43, in 4-player, each gets 10, with 3 extra neutrals; in 5-, each gets 8, and the extra 3 become neutral as well; in 6-, each gets 7, and the extra 1 becomes neutral; in 7-, each gets 6, and the extra 1 becomes neutral; and in 8-, each gets 5, and the extra 3 become neutrals.

With all cities neutral (twelve, I think), we have 40 in the pool: in 2-player games, each gets 13, with 14 extra neutrals; in 3-, each gets 13, plus 1 extra neutral; in 4-, each gets 10, no extras; in 5-, each gets 8, no extras; in 6-, each gets 6, with 4 extra neutrals; in 7-, each gets 5, plus 5 extra neutrals; in 8-, each gets 5, no extras.

[The Bison King]

I shall ponder this for a bit.

[MrBenn]

I've updated my Bonus Probabilities Spreadsheet to account for starting positions, but am having trouble uploading it anywhere

[mattattam]

Another thing to think about Bison is if you decide on making 8-9 territories neutral would you:

1. Want to have the neutral territories randomly picked each game or

2. Would you want to pick a specific 8-9 territories to help balance the probabilities of dropping a bonus? And if so which 8-9 territories would be best?

[ender516]

Off hand, I cannot think of an easy way to make those 8 or 9 regions neutral without fixing their locations. I outlined the numbers to meet your proposal, but personally, I would rather go with the neutral cities. It makes the players work for the privilege of using the roads to scoot across the map.

[MrBenn]

I've updated my Bonus Probabilities Spreadsheet to account for starting positions, but am having trouble uploading it anywhere

Got it.... http://www.fileden.com/files/2009/1/9/2259283//BonusProbability2.xls

Play around with the bonus spreadsheet a bitand see if there is some combination of neutral starts, or larger starting position groups that help. It might be that by ADDING terrs to the starting group, you can increase the number of dropped territories to 19 or 20 for 1v1 games (which is better than 18)

[mattattam]

I've updated my Bonus Probabilities Spreadsheet to account for starting positions, but am having trouble uploading it anywhere

Got it.... http://www.fileden.com/files/2009/1/9/2259283//BonusProbability2.xls

Play around with the bonus spreadsheet a bitand see if there is some combination of neutral starts, or larger starting position groups that help. It might be that by ADDING terrs to the starting group, you can increase the number of dropped territories to 19 or 20 for 1v1 games (which is better than 18)

19 or 20 is just as bad and harder to do since you have to add territories.

Ender - I definitely agree that making a lot of the cities neutral would be a good idea.

To through a possibility out there you could make these 8 territories neutral:
7 cities-
Northern frontier
Denmarn
Arleus
Ifnal
South Lyalia
Hellangar
Dalmus

Last 1 is Sarle. This would help by taking way the possibility of dropping the green bonus Itherenia and would keep the southeast part of the map open.

[MrBenn]

I've updated my Bonus Probabilities Spreadsheet to account for starting positions, but am having trouble uploading it anywhere

Got it.... http://www.fileden.com/files/2009/1/9/2259283//BonusProbability2.xls

Play around with the bonus spreadsheet a bitand see if there is some combination of neutral starts, or larger starting position groups that help. It might be that by ADDING terrs to the starting group, you can increase the number of dropped territories to 19 or 20 for 1v1 games (which is better than 18)

19 or 20 is just as bad and harder to do since you have to add territories.

No, you've misunderstood my point. By adding territories to the starting position groups (not to the map itself), you reduce the number of neutrals dropped in 1v1 games. This is what has created the 18 terr issue in the first place.

You're also incorrect in stating that 19 or 20 are just as bad - either option means that the first player has to take more than one terr to reduce the second players deployment, and reduces the advantage of going first.

[mattattam]

No, you've misunderstood my point. By adding territories to the starting position groups (not to the map itself), you reduce the number of neutrals dropped in 1v1 games. This is what has created the 18 terr issue in the first place.

You're also incorrect in stating that 19 or 20 are just as bad - either option means that the first player has to take more than one terr to reduce the second players deployment, and reduces the advantage of going first.

I see your point on adding territories to the starting group and not on the map itself. Understood

For the starting positions being bumped to 19-20 I see it as a slight improvement in the wrong direction, lol. It does make it harder to drop your oponnents territories to 17 giving them one less to deploy but what about dropping a bonus? Having even more territories in 2-4 player game types is especially bad for this map due to how many bonus' a player can drop and only creates a greater 1st turn advantage.

[ender516]

I've updated my Bonus Probabilities Spreadsheet to account for starting positions, but am having trouble uploading it anywhere

Got it.... http://www.fileden.com/files/2009/1/9/2259283//BonusProbability2.xls

Play around with the bonus spreadsheet a bitand see if there is some combination of neutral starts, or larger starting position groups that help. It might be that by ADDING terrs to the starting group, you can increase the number of dropped territories to 19 or 20 for 1v1 games (which is better than 18)

Thanks for the upgrade. This sheet is more powerful than the last, and I like the red highlight on bad numbers of dropped territories like 18. Someday, I hope to create a tool that goes a step beyond this, which analyzes an XML file, firstly, to extract the numbers you need for this sheet, and secondly, to recognize the actual interactions between the regions in the starting positions and the zones which provide bonuses. That way, there would be no need to panic about the probability of dropping a 3-region zone on a given map if all such zones were split by starting positions.